Fast prediction of plasma instabilities with sparse-grid-accelerated optimized dynamic mode decomposition
Kevin Gill, Ionut-Gabriel Farcas, Silke Glas, Benjamin J. Faber
TL;DR
This work tackles the computational bottleneck of many-query tasks in high-dimensional parametric gyrokinetic simulations by integrating sparse-grid interpolation with $(L)$-Leja points and optimized dynamic mode decomposition (optDMD) to build parametric reduced-order models (ROMs). The approach yields large online speedups (often orders of magnitude) while accurately predicting dominant instability characteristics and full distribution-function structure across parameter variations, demonstrated on CBC ITG and ETG pedestal scenarios. A key contribution is showing that only a modest number of high-fidelity simulations (as few as 28 for six parameters) can suffice to construct accurate, interpolative parametric ROMs, thanks to the slow growth and nesting properties of $(L)$-Leja sparse grids. The results indicate that sparse-grid-accelerated parametric optDMD ROMs can enable otherwise intractable many-query analyses in fusion plasma research, including design, optimization, and uncertainty quantification tasks, with broad applicability beyond gyrokinetics.
Abstract
Parametric data-driven reduced-order models (ROMs) that embed dependencies in a large number of input parameters are crucial for enabling many-query tasks in large-scale problems. These tasks, including design optimization, control, and uncertainty quantification, are essential for developing digital twins in real-world applications. However, standard grid-based data generation methods are computationally prohibitive due to the curse of dimensionality. This paper investigates efficient training of parametric data-driven ROMs using sparse grid interpolation with (L)-Leja points, specifically targeting scenarios with higher-dimensional input parameter spaces. (L)-Leja points are nested and exhibit slow growth, resulting in sparse grids with low cardinality in low-to-medium dimensional settings, making them ideal for large-scale, computationally expensive problems. Focusing on gyrokinetic simulations of plasma micro-instabilities in fusion experiments as a representative real-world application, we construct parametric ROMs for the full 5D gyrokinetic distribution function via optimized dynamic mode decomposition (optDMD) and sparse grids based on (L)-Leja points. We perform detailed experiments in two scenarios: First, the Cyclone Base Case benchmark assesses optDMD ROM prediction capabilities beyond training time horizons and across variations in the binormal wave number. Second, for a real-world electron-temperature-gradient-driven micro-instability simulation with six input parameters, we demonstrate that a predictive parametric optDMD ROM that is up to three orders of magnitude cheaper to evaluate can be constructed using only 28 high-fidelity gyrokinetic simulations, enabled by the use of sparse grids. In the broader context of fusion research, these results demonstrate the potential of sparse grid-based parametric ROMs to enable otherwise intractable many-query tasks.